Terrains have a key role in making outdoor virtual scenes believable and immersive as they form the support for every other natural element in the scene. Although important, terrains are often given limited interactivity in real-time applications. However, in nature, terrains are dynamic and interact with the rest of the environment changing shape on different levels, from tracks left by a person running on a gravel soil (micro-scale), to avalanches on the side of a mountain (macro-scale). The challenge in representing dynamic terrains correctly is that the soil that forms them is vastly heterogeneous and behaves differently depending on its composition. This heterogeneity introduces difficulties at different levels in dynamic terrains simulations, from modelling the large amount of different elements that compose the oil to simulating their dynamic behaviour. This work presents a novel framework to simulate multi-material dynamic terrains by taking into account the soil composition and its heterogeneity. In the proposed framework soil information is obtained from a material description map applied to the terrain mesh. This information is used to compute deformations in the area of interaction using a novel mathematical model based on diffusion theory. The deformations are applied to the terrain mesh in different ways depending on the distance of the area of interaction from the camera and the soil material. Deformations away from the camera are simulated by dynamically displacing normals. While deformations in a neighbourhood of the camera are represented by displacing the terrain mesh, which is locally tessellated to better fit the displacement. For gravel based soils the terrain details are added near the camera by reconstructing the meshes of the small rocks from the texture image, thus simulating both micro and macro-structure of the terrain. The outcome of the framework is a realistic interactive dynamic terrain animation in real-time.